from research import *
s=begin(1011,'Integral Esau measurement basis','Is the nine-measurement inverse an integer change of coordinates?',{},['C1009','C1010'])
from algebra import Matrix
p=json.loads((ROOT/'model/esau_joint_measurements.json').read_text());idx=[0,1,2,3,4,5,8,10,11];M=Matrix([p['matrix'][i] for i in idx]);y=Matrix([p['measurements'][i] for i in idx]);inverse=M.inv()
a=artifact('model/esau_unimodular_basis.json',json.dumps(clean({'selected_rows':idx,'matrix':M.tolist(),'measurements':list(y),'inverse':inverse.tolist(),'determinant':M.det()}),indent=2)+'\n')
finish(s,{'basis':a,'determinant':M.det(),'reconstructed':list(inverse*y)},'The compact Esau basis has determinant1 and an integer inverse. It changes coordinates without fractional adjustment; it does not reduce nine independent numbers to fewer than nine.','Compare with the complete clean-plus-unclean walk basis.',{'unimodular':M.det()==1,'integral_inverse':all(x.denominator==1 for x in inverse),'recover_counts':list(inverse*y)==[200,20,200,20,40,10,30,20,10]})